Finite Group Databasebeta

← #14430954

Subgroups — #14430954

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5729C211yesmaximal, characteristic
2#11752523C211yesmaximal, characteristic
3#11751195C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5#11747489C211yesmaximal, characteristic
6D3×#3942C211yesmaximal, characteristic
7#11747454C211yesmaximal, characteristic
8#11747435C211yesmaximal, characteristic
9#11747295C211yesmaximal, characteristic, complemented
10#11747293C211yesmaximal, characteristic, complemented
11#11747292C211yesmaximal, characteristic, complemented
12#11747290C211yesmaximal, characteristic, complemented
13#11746993C211yesmaximal, characteristic
14#11746967C211yesmaximal, characteristic, complemented
15#11746919C211yesmaximal, characteristic, complemented
16#10615211—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C5×#946—21no—
21C5×#944—21no—
22C5×#896—21no—
23C5×#892C2211yescharacteristic
24C5×D3×C4⋊C4C2211yescharacteristic
25C5×#890C2211yescharacteristic
26C5×#889—21no—
27C5×#888C2211yescharacteristic
28C5×#872C2211yescharacteristic
29C5×#870C2211yescharacteristic
30C3×C4×Dic10C2211yescharacteristic
31#91400—21no—
32#91398—21no—
33#91340C2211yescharacteristic
34#91338C2211yescharacteristic
35Dic3×Dic10C2211yescharacteristic
36#91325—21no—
37#91323—21no—
38C2×#6650C2211yescharacteristic
39C2×D3×#168C2211yescharacteristic
40#91094C2211yescharacteristic
41#91094C2211yescharacteristic
42#91092C2211yescharacteristic
43#91092C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C3×#3942C2211yescharacteristic
46C3×#3942C2211yescharacteristic
47C3×#3939C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×C4⋊#168C2211yescharacteristic
50#90989C2211yescharacteristic
51#90988C2211yescharacteristic
52#90986C2211yescharacteristic
53#90985C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55Dic3⋊#168C2211yescharacteristic
56#90975C2211yescharacteristic
57#90975C2211yescharacteristic
58#90970C2211yescharacteristic
59#90970C2211yescharacteristic
60#81110—51nomaximal, Hall
61C5×#544—31no—
62#65850—31no—
63#65383—31no—
64#65383—31no—
65#65380—31no—
66#65380D311yescharacteristic, complemented
67#65352—31no—
68#65352—31no—
69#65352—31no—
70#65352—31no—
71#65293—31no—
72#65288—31no—
73#65287—31no—
74C2×#3942—31no—
75#65253—31no—
76C2×C3×C5×Q8—21no—
77C2×Dic30C2311yescharacteristic
78C2×C4×C5×D3—21no—
79C2×C4×C5×D3C2311yescharacteristic
80C2×C5×Dic6—21no—
81C2×C3×Dic10C2311yescharacteristic
82C2×#1204—21no—
83C2×D3×Dic5—21no—
84D3×Dic10—22no—
85D3×Dic10Q814yescomplemented
86C3×C5×C4⋊C4—21no—
87C3×C5×C4⋊C4C2311yescharacteristic
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C42×C5C2311yescharacteristic
90C4⋊Dic15C2311yescharacteristic
91#6712—21no—
92C4×Dic15—21no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×(C2×D3)⋊C4—21no—
96C5×(C2×D3)⋊C4D411yescharacteristic
97C5×(C2×D3)⋊C4D411yescharacteristic
98C5×C4⋊Dic3—21no—
99C5×C4⋊Dic3C2311yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4D411yescharacteristic
107C5×Dic3⋊C4D411yescharacteristic
108C4×C5×Dic3—21no—
109C4×C5×Dic3C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×C4×Dic5—21no—
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115#6669—21no—
116#6668—21no—
117(C2×D3)⋊Dic5—21no—
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6650—22no—
122D3×#168—22no—
123#5729D511yescharacteristic
124#5572—51no—
125C3×#477—51no—
126#5094—51no—
127#5022—51no—
128#4881—51no—
129#4880—51no—
130#4877—51no—
131#4875—51no—
132#4839—51no—
133#4829—51no—
134#4802—51no—
135D3×#103—51no—
136#4796—51no—
137#4791—51no—
138C22×Dic10—31no—
139C5×C4⋊Q8—31no—
140C5×C4⋊Q8—61no—
141C5×C4⋊Q8C2×D311yescharacteristic
142C5×#125—31no—
143C5×#125—31no—
144C5×#125—61no—
145C5×C22⋊Q8—61no—
146C5×C22⋊Q8—61no—
147C5×#117—31no—
148C5×#117—31no—
149C2×C5×C4⋊C4—31no—
150#4072—31no—
151C2×#681—31no—
152C22×#168—31no—
153#4033—61no—
154#4033—61no—
155#4023—61no—
156#4023—61no—
157C4×Dic10—31no—
158C4×Dic10—31no—
159C4×Dic10—31no—
160C4×Dic10C2×D311yescharacteristic
161#3942—31no—
162#3942—31no—
163#3942—31no—
164#3942—31no—
165#3942—31no—
166#3942—31no—
167#3942C2×D311yescharacteristic
168#3942C2×D311yescharacteristic
169#3940—31no—
170#3940—31no—
171#3940—31no—
172#3940—31no—
173#3939—31no—
174#3939—31no—
175#3939C2×D311yescharacteristic
176#3939C2×D311yescharacteristic
177C4⋊#168—31no—
178C4⋊#168—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181#3082—151noSylow
182C22×C5×D3C2×D411yescharacteristic
183C3×C5×Q8—81no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2411yescharacteristic
189C2×Dic15—21no—
190C2×Dic15—21no—
191Dic30—21no—
192Dic30C2×Q812yes—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3C2×D411yescharacteristic
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C4×C5×D3—81no—
199C4×C5×D3C2×Q812yes—
200C4×C5×D3#4112yes—
201C5×Dic6—81no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C3×Dic10—21no—
205C3×Dic10C2×Q812yes—
206#1204—24no—
207D3×Dic5—24no—
208C3⋊#168—21no—
209C3⋊#168—21no—
210C3×#168—21no—
211C3×#168—21no—
212C2×D3×Q8—51no—
213C3×C4⋊Q8C2×D511yescharacteristic
214C3×C4×Q8—51no—
215#946—21no—
216Q8×Dic3—51no—
217#944—21no—
218C2×ΓL(1,𝔽25)—51no—
219C2×D3×C8—51no—
220#896—21no—
221#892—51no—
222#892—101no—
223#892C2×D511yescharacteristic
224D3×C4⋊C4C2×D511yescharacteristic
225#890C2×D511yescharacteristic
226#889—21no—
227#888C2×D511yescharacteristic
228#887—51no—
229#887—101no—
230#872—101no—
231#872C2×D511yescharacteristic
232#870C2×D511yescharacteristic
233C4×Dic6—51no—
234C4×Dic6—101no—
235C3×#107—51no—
236C3×#107—51no—
237C3×C4⋊C8—51no—
238C3×#103—51no—
239C3×#103—51no—
240#835—51no—
241#835—51no—
242#818—51no—
243#817—51no—
244#816—51no—
245#816—51no—
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248#810—51no—
249#810—51no—
250#808—51no—
251#808—51no—
252#808—51no—
253#807—51no—
254C4⋊(C3⋊C8)—51no—
255C2×C5×Q8—21no—
256C2×C5×Q8—61no—
257C22×C4×C5—31no—
258C22×C4×C5—61no—
259C22×Dic5—61no—
260C2×Dic10—31no—
261C2×Dic10—34no—
262C2×Dic10—62no—
263C2×Dic10—61no—
264C2×Dic10C22×D311yescharacteristic
265C5×C4⋊C4—21no—
266C5×C4⋊C4—31no—
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—61no—
271C5×C4⋊C4—61no—
272C5×C4⋊C4—61no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—31no—
279C5×C22⋊C4—31no—
280C5×C22⋊C4—61no—
281C42×C5—31no—
282C42×C5—61no—
283C42×C5C22×D311yescharacteristic
284C22⋊Dic5—61no—
285C4⋊Dic5—31no—
286C4⋊Dic5C22×D311yescharacteristic
287#683—21no—
288#683—61no—
289#683—61no—
290#683—61no—
291C4×Dic5—21no—
292C4×Dic5—61no—
293C4×Dic5—61no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296#681—62no—
297C2×#168—31no—
298C2×#168—31no—
299C2×#168—62no—
300C2×#168C22×D311yescharacteristic
301C2×#168C22×D311yescharacteristic
302#544—31no—
303#519—151no—
304#479—151no—
305#479—151no—
306#479—151no—
307#479—151no—
308#477—51no—
309#477—151no—
310#475—151no—
311#475—151no—
312#428—151no—
313#427—151no—
314#424—151no—
315#419—151no—
316C2×#103—151no—
317C22×C3×C5C22×D411yescharacteristic
318C2×C5×D3—21no—
319C2×C5×D3—21no—
320C2×C5×D3C22⋊Q812yes—
321C3×C4×C5—21no—
322C3×C4×C5—21no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5C22×Q811yescharacteristic
326C3×C4×C5C2×#4111yescharacteristic
327Dic15—22no—
328Dic15—41no—
329C3×Dic5—22no—
330C3×Dic5—41no—
331C5×Dic3—21no—
332C5×Dic3—21no—
333C5×Dic3—41no—
334C5×Dic3—41no—
335C5×Dic3C22⋊Q812yes—
336C2×C3×Q8—21no—
337C2×C3×Q8—51no—
338D3×Q8—54no—
339D3×Q8—102no—
340C2×C4×D3—21no—
341C2×C4×D3—101no—
342C2×C4×D3C22×D511yescharacteristic
343C2×Dic6—21no—
344C2×Dic6—51no—
345C2×Dic6—101no—
346C2×C3×C8—51no—
347C2×C3×C8—51no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4—101no—
351C3×C4⋊C4C22×D511yescharacteristic
352C3×C4⋊C4C22×D511yescharacteristic
353C3×C42—101no—
354C3×C42C22×D511yescharacteristic
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—101no—
357(C2×D3)⋊C4C22⋊D511yescharacteristic
358(C2×D3)⋊C4C22⋊D511yescharacteristic
359C4⋊Dic3—21no—
360C4⋊Dic3—51no—
361C4⋊Dic3—101no—
362C4⋊Dic3C22×D511yescharacteristic
363C4⋊Dic3C22×D511yescharacteristic
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4C22⋊D511yescharacteristic
372Dic3⋊C4C22⋊D511yescharacteristic
373C4×Dic3—21no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3C22×D511yescharacteristic
379C2×C3⋊C8—51no—
380C2×C3⋊C8—51no—
381ΓL(1,𝔽25)—102no—
382D3×C8—102no—
383C23×C5—31no—
384C5×Q8—81no—
385C5×Q8—241no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—31no—
389C2×C4×C5—32no—
390C2×C4×C5—32no—
391C2×C4×C5—31no—
392C2×C4×C5—31no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—241no—
396C2×C4×C5D3×D411yescharacteristic
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—64no—
402C2×Dic5—61no—
403C2×Dic5—61no—
404Dic10—21no—
405Dic10—32no—
406Dic10—64no—
407Dic10—61no—
408Dic10D3×Q812yes—
409#168—21no—
410#168—21no—
411#168—61no—
412#168—61no—
413C22×Q8—151no—
414C2×M16—151no—
415C22×C8—151no—
416C4⋊Q8—31no—
417C4⋊Q8—61no—
418C4⋊Q8D3×D511yescharacteristic
419#125—31no—
420#125—31no—
421#125—61no—
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C4×Q8—51no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—301no—
429C4×Q8—301no—
430#117—31no—
431#117—31no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—31no—
436#107—51no—
437#107—51no—
438#107—151no—
439#107—151no—
440#106—151no—
441#106—151no—
442#106—151no—
443#106—151no—
444C4⋊C8—51no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—51no—
449#103—51no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#103—151no—
455#103—151no—
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459C5×D3—22no—
460C22×D3C2×C22⋊D511yescharacteristic
461C3×Q8—52no—
462C3×Q8—81no—
463C3×Q8—101no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—101no—
467C2×C3×C4—101no—
468C2×C3×C4C2×C22⋊D511yescharacteristic
469C2×C3×C4C2×C22⋊D511yescharacteristic
470C2×C3×C4C23×D511yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—101no—
474C2×Dic3—101no—
475C2×Dic3C2×C22⋊D511yescharacteristic
476C2×Dic3C2×C22⋊D511yescharacteristic
477C2×Dic3C2×C22⋊D511yescharacteristic
478C4×D3—81no—
479C4×D3—104no—
480C4×D3Q8×D512yes—
481C4×D3#71312yes—
482Dic6—52no—
483Dic6—81no—
484Dic6—101no—
485Dic6—104no—
486C3×C8—101no—
487C3×C8—101no—
488C3⋊C8—101no—
489C3⋊C8—101no—
490C22×C5—32no—
491C22×C5—61no—
492C22×C5—61no—
493C22×C5C2×D3×D411yescharacteristic
494C4×C5—21no—
495C4×C5—21no—
496C4×C5—32no—
497C4×C5—41no—
498C4×C5—41no—
499C4×C5—61no—
500C4×C5—61no—
501C4×C5—121no—
502C4×C5—121no—
503C4×C5C2×D3×Q811yescharacteristic
504C4×C5D3×#4111yescharacteristic
505Dic5—22no—
506Dic5—41no—
507Dic5—62no—
508Dic5—121no—
509C2×Q8—21no—
510C2×Q8—51no—
511C2×Q8—61no—
512C2×Q8—154no—
513C2×Q8—151no—
514C2×Q8—301no—
515C2×Q8—302no—
516C22×C4—31no—
517C22×C4—61no—
518C22×C4—301no—
519M16—302no—
520C2×C8—51no—
521C2×C8—51no—
522C2×C8—151no—
523C2×C8—151no—
524C2×C8—302no—
525C4⋊C4—21no—
526C4⋊C4—31no—
527C4⋊C4—31no—
528C4⋊C4—31no—
529C4⋊C4—31no—
530C4⋊C4—51no—
531C4⋊C4—61no—
532C4⋊C4—61no—
533C4⋊C4—61no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—101no—
538C4⋊C4—151no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4—301no—
542C4⋊C4C2×D3×D511yescharacteristic
543C4⋊C4C2×D3×D511yescharacteristic
544C22⋊C4—31no—
545C22⋊C4—31no—
546C22⋊C4—61no—
547C22⋊C4—301no—
548C42—31no—
549C42—61no—
550C42—101no—
551C42—301no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42C2×D3×D511yescharacteristic
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3C22×C22⋊D511yescharacteristic
558C2×D3—21no—
559C2×D3—21no—
560C2×D3#409212yes—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—41no—
564C3×C4—41no—
565C3×C4—102no—
566C3×C4—201no—
567C3×C4C2×Q8×D511yescharacteristic
568C3×C4C2×#71311yescharacteristic
569Dic3—21no—
570Dic3—21no—
571Dic3—41no—
572Dic3—41no—
573Dic3—102no—
574Dic3—201no—
575Dic3#409212yes—
576C2×C5—62no—
577C2×C5D3×C22⋊Q811yescharacteristic
578C2×C5#576611yescharacteristic
579C2×C5#577511yescharacteristic
580C23—31no—
581Q8—52no—
582Q8—81no—
583Q8—101no—
584Q8—152no—
585Q8—241no—
586Q8—304no—
587Q8—301no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—31no—
591C2×C4—32no—
592C2×C4—32no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—101no—
598C2×C4—101no—
599C2×C4—241no—
600C2×C4—304no—
601C2×C4—301no—
602C2×C4—301no—
603C2×C4D3×C22⋊D511yescharacteristic
604C2×C4D3×C22⋊D511yescharacteristic
605C2×C4C22×D3×D511yescharacteristic
606C8—101no—
607C8—101no—
608C8—301no—
609C8—301no—
610C2×C3C2×#409211yescharacteristic
611C2×C3#6617011yescharacteristic
612C2×C3#6617211yescharacteristic
613D3—22no—
614C5#8111011yescharacteristic, complemented, Sylow
615C22—32no—
616C22—61no—
617C22—61no—
618C22C2×D3×C22⋊D511yescharacteristic
619C4—21no—
620C4—21no—
621C4—32no—
622C4—41no—
623C4—41no—
624C4—61no—
625C4—61no—
626C4—102no—
627C4—121no—
628C4—121no—
629C4—201no—
630C4—302no—
631C4—601no—
632C4D3×Q8×D511yescharacteristic
633C4D3×#71311yescharacteristic
634C3#1061521111yescharacteristic, complemented, Sylow
635C2—62no—
636C2#1175472011yescharacteristic
637C2#1175510511yescharacteristic
638C2D3×#409211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #11751195C2semidirect
4. C3×#65380C2semidirect
9. #11747295C2semidirect
10. #11747293C2semidirect
11. #11747292C2semidirect
12. #11747290C2semidirect
14. #11746967C2semidirect
15. #11746919C2semidirect
66. #65380D3semidirect
85. D3×Dic10Q8semidirect
556. C3×C5#3082semidirect
614. C5#81110semidirect
634. C3#10615211semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#57292
#117525232
#117511952
C3×#653802
#117474892
D3×#39422
#117474542
#117474352
#117472952
#117472932
#117472922
#117472902
#117469932
#117469672
#117469192
#106152113
#811105